A constructive procedure to design a single linear functional observer for a time-invariant linear system is given. The proposed procedure is simple and is not based on the solution of a Sylvester equation or on the use of canonical state space forms. Both stable observers or fixed poles observers problems are considered for minimality.

We consider the uniqueness of the inverse problem for a semilinear elliptic differential equation with Dirichlet condition. The necessary and sufficient condition of a unique solution is obtained. We improved the results obtained by Isakov and Sylvester (1994) for the same problem.

This paper presents the solution of the constrained Sylvester equation associated to linear descriptor systems. This problem has been recently studied in [1], where sufficient conditions for the existence of the solution are given. In the present paper, a simple and direct method is developed to solve this problem. This method shows that the conditions given in [1] are necessary and sufficient.

We present a direct algorithm for computing an orthogonal similarity transformation which interchanges neighboring diagonal blocks in a matrix in real Schur form. The algorithm does not require the solution of the associated Sylvester equation. Numerical tests suggest the backward stability of the scheme.

Combination of real and imaginary parts (CRI) method is an efficient for solving a class large sparse linear systems with complex symmetric positive semi-definite coefficient matrices. In this work we will extend CRI approach to determine the approximate solution Sylvester equation We show that new algorithm converges unconditionally unique exact matrix equation. end test scheme by some numeric...

For modeling data matrices, this paper introduces Probabilistic Co-Subspace Addition (PCSA) model by simultaneously capturing the dependent structures among both rows and columns. Briefly, PCSA assumes that each entry of a matrix is generated by the additive combination of the linear mappings of two low-dimensional features, which distribute in the row-wise and column-wise latent subspaces resp...